Depending which program you choose, the steps may be different, but all you essentially have to do is (I'll use Wondershare for illustration purposes):

1. Download and install one of the programs above. Launch the program on your computer.

2. Connect your Android to your computer (with the recovery program installed and program running) with a USB cable.

3. Enable USB Debugging on your Android. To do this, you need to have access to the Developer Options in your main Settings menu. If you don't, just go to About Phone, scroll down to Build Number and start tapping repeatedly. You'll now get access to Developer Options in the main Settings menu (just above About Phone). Go into Developer Options, scroll down to USB Debugging (or Android Debugging, depending on your ROM) and check the box.

4. Follow the prompts in the recovery program to scan or analyze your Android's memory.

5. Once the process is complete you will have access to browse and preview the data stored on your Android device (whether it has been ''deleted'' or not. As long as the particular part of memory on which is was originally stored has not been saved over, you can still get the data back. This is why it's important to act quickly if you've lost data.

6. Simply locate your text message folder (or however the particular program presents your data), select the messages you wish to recover and either use the Recover action in the program to put them back on your device or save them to your computer for safe keeping.

Note: if you want to complete this process without a PC, chances are you will need root access on your device and more than likely a paid recovery app. In any case, it's easier and free to use a computer. 

Ok, so maybe you've learned your lesson, maybe you haven't. If you're not into paying for any of the programs above long-term or simply don't like the free options, your best bet is to ensure you don't have a need for them again. This means backing up your messages from now on. It's so simple it only takes five minutes to save yourself the pain of having to deal with this situation again. I use a free app called SMS Backup & Restore. It's straightforward, looks nice and works perfectly: basically all you need for this type of operation. Check out the screenshots below for the walkthrough.